{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T06:25:06Z","timestamp":1761719106421,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T00:00:00Z","timestamp":1642896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61803061, 61906026","61771081, 61703347"],"award-info":[{"award-number":["61803061, 61906026","61771081, 61703347"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["XDJK2020B010"],"award-info":[{"award-number":["XDJK2020B010"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation research group of universities in Chongqing","award":["NA"],"award-info":[{"award-number":["NA"]}]},{"name":"Chongqing Natural Science Foundation","award":["cstc2020jcyj-msxmX0577, cstc2020jcyj-msxmX0634, cstc2019jcyj-msxmX0110, cstc2021jcyj-msxmX0416"],"award-info":[{"award-number":["cstc2020jcyj-msxmX0577, cstc2020jcyj-msxmX0634, cstc2019jcyj-msxmX0110, cstc2021jcyj-msxmX0416"]}]},{"name":"&quot;Chengdu-Chongqing Economic Circle&quot; innovation funding of Chongqing Municipal Education Commission","award":["KJCXZD2020028"],"award-info":[{"award-number":["KJCXZD2020028"]}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["KJQN202000602"],"award-info":[{"award-number":["KJQN202000602"]}]},{"name":"Ministry of Education China Mobile Research Fund","award":["MCM 20180404"],"award-info":[{"award-number":["MCM 20180404"]}]},{"name":"Special key project of Chongqing technology innovation and application development","award":["cstc2019jscx-zdztzx0068"],"award-info":[{"award-number":["cstc2019jscx-zdztzx0068"]}]},{"name":"Innovation Project of Chongqing Overseas Students Entrepreneurial Innovation Support program","award":["cx2018074"],"award-info":[{"award-number":["cx2018074"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>With the increase in the complexity and informatization of power grids, new challenges, such as access to a large number of distributed energy sources and cyber attacks on power grid control systems, are brought to load-frequency control. As load-frequency control methods, both aggregated distributed energy sources (ADES) and artificial intelligence techniques provide flexible solution strategies to mitigate the frequency deviation of power grids. This paper proposes a load-frequency control strategy of ADES-based reinforcement learning under the consideration of reducing the impact of denial of service (DoS) attacks. Reinforcement learning is used to evaluate the pros and cons of the proposed frequency control strategy. The entire evaluation process is realized by the approximation of convex neural networks. Convex neural networks are used to convert the nonlinear optimization problems of reinforcement learning for long-term performance into the corresponding convex optimization problems. Thus, the local optimum is avoided, the optimization process of the strategy utility function is accelerated, and the response ability of controllers is improved. The stability of power grids and the convergence of convex neural networks under the proposed frequency control strategy are studied by constructing Lyapunov functions to obtain the sufficient conditions for the steady states of ADES and the weight convergence of actor\u2013critic networks. The article uses the IEEE14, IEEE57, and IEEE118 bus testing systems to verify the proposed strategy. Our experimental results confirm that the proposed frequency control strategy can effectively reduce the frequency deviation of power grids under DoS attacks.<\/jats:p>","DOI":"10.3390\/a15020034","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:32:52Z","timestamp":1642969972000},"page":"34","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Convex Neural Networks Based Reinforcement Learning for Load Frequency Control under Denial of Service Attacks"],"prefix":"10.3390","volume":"15","author":[{"given":"Fancheng","family":"Zeng","sequence":"first","affiliation":[{"name":"College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9562-3865","authenticated-orcid":false,"given":"Guanqiu","family":"Qi","sequence":"additional","affiliation":[{"name":"Computer Information Systems Department, State University of New York at Buffalo State, Buffalo, NY 14222, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiqin","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Hu","sequence":"additional","affiliation":[{"name":"Computer Information Systems Department, State University of New York at Buffalo State, Buffalo, NY 14222, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew","family":"Haner","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Computer and Information Science, Mansfield University of Pennsylvania, Mansfield, PA 16933, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1109\/TSG.2014.2314494","article-title":"Stability Analysis of Networked Control in Smart Grids","volume":"6","author":"Singh","year":"2015","journal-title":"IEEE Trans. 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